Mathematical Treasures - Jiuzhang suanshu

This page is from a sixteenth century Ming dynasty edition of the Jiuzhang suanshu (Nine Chapters on the Mathematical Art). The work was originally written around the beginning of our era, but the extant copies we have today all stem from an edition and commentary prepared by Liu Hui in the third century. This illustration explains Liu's exhaustion method for determining pi. He obtained a value of 3.14024. A successor, astronomer-mathematician Zu Chongzhi (429-501) extended the method further and obtained a lower bound of 3.1415926 for pi and an upper bound of 3.1415927. For more details on Liu Hui's calculation, see Victor Katz, ed., The Mathematics of Egypt, Mesopotamia, China, India, and Islam: A Sourcebook (Princeton University Press, 2007), pp. 235-240.